What are the solutions to the equation (x^2-64)^2+(x^2+5x-104)^2=0 ?

The solutions to the equation (x^2-64)^2+(x^2+5x-104)^2=0 are x=8,x=-21/2+i 5/2 ,x=-21/2-i 5/2

Find the zeros of (x^2-64)^2+(x^2+5x-104)^2=0

The zeros of (x^2-64)^2+(x^2+5x-104)^2=0 are x=8,x=-21/2+i 5/2 ,x=-21/2-i 5/2

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(x^{2} - 64)^{2} + (x^{2} + 5 x - 104)^{2} = 0

x = 8, x = - \frac{21}{2} + i \frac{5}{2}, x = - \frac{21}{2} - i \frac{5}{2}

Solution steps

(x^{2} - 64)^{2} + (x^{2} + 5 x - 104)^{2} = 0

Factor

(x^{2} - 64)^{2} + (x^{2} + 5 x - 104)^{2} : (x - 8)^{2} (2 x^{2} + 42 x + 233)

(x - 8)^{2} (2 x^{2} + 42 x + 233) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 8 = 0 or 2 x^{2} + 42 x + 233 = 0

Solve

x - 8 = 0 : x = 8

Solve

2 x^{2} + 42 x + 233 = 0 : x = - \frac{21}{2} + i \frac{5}{2}, x = - \frac{21}{2} - i \frac{5}{2}

The solutions are

x = 8, x = - \frac{21}{2} + i \frac{5}{2}, x = - \frac{21}{2} - i \frac{5}{2}

5 x^{3} - 7 x + 2

x^{5} - 2 x^{4} + 2 x^{3} - 4 x^{2} - 2 = 0

x^{4} + 2 x^{2} + 1

4 x^{4} - 2 x^{2} + 1 = 0

x^{3} - x^{2} - x + 1

What are the solutions to the equation (x^2-64)^2+(x^2+5x-104)^2=0 ?
The solutions to the equation (x^2-64)^2+(x^2+5x-104)^2=0 are x=8,x=-21/2+i 5/2 ,x=-21/2-i 5/2
Find the zeros of (x^2-64)^2+(x^2+5x-104)^2=0
The zeros of (x^2-64)^2+(x^2+5x-104)^2=0 are x=8,x=-21/2+i 5/2 ,x=-21/2-i 5/2